Kernel Machines With Missing Responses

TL;DR

This paper introduces kernel machines capable of handling missing responses, providing robust estimators for regression and classification with theoretical guarantees and empirical validation.

Contribution

It develops kernel machine methods that effectively manage missing responses, including doubly-robust variants with proven consistency and convergence rates.

Findings

Kernel machines using complete cases perform well with missing data.

Doubly-robust kernel machines offer improved robustness.

Empirical results demonstrate the effectiveness of the proposed methods.

Abstract

Missing responses is a missing data format in which outcomes are not always observed. In this work we develop kernel machines that can handle missing responses. First, we propose a kernel machine family that uses mainly the complete cases. For the quadratic loss, we then propose a family of doubly-robust kernel machines. The proposed kernel-machine estimators can be applied to both regression and classification problems. We prove oracle inequalities for the finite-sample differences between the kernel machine risk and Bayes risk. We use these oracle inequalities to prove consistency and to calculate convergence rates. We demonstrate the performance of the two proposed kernel machine families using both a simulation study and a real-world data analysis.